Question

In Problems 15–18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

$\left(A\right)\frac{x^2}{4}-y^2=1\left(B\right)x^2-\frac{y^2}{4}=1\left(C\right)\frac{y^2}{4}-x^2=1\left(D\right)y^2-\frac{x^2}{4}=1$

Graph:

Short answer

The equation of given graph is:$\left(D\right)y^2-\frac{x^2}{4}=1$

Step-by-step solution

Step 1. Given information  

Equations:

$\left(A\right)\frac{x^2}{4}-y^2=1\left(B\right)x^2-\frac{y^2}{4}=1\left(C\right)\frac{y^2}{4}-x^2=1\left(D\right)y^2-\frac{x^2}{4}=1$

Graph:

Step 2. Required to find  

Match the graph to its equation.

Step 3. Matching the graph to its equation 

Substitute values of points on the graph and see if the equation holds good.

In the given graph, take point $(x,y)=(0,1)$, only equation (D) satisfies and hence, it is the right match.